Po waves from OBS observation
Two ocean bottom seismometers (OBSs) data sets were used: one from active seismic surveys (Fujie et al. 2013) and the other from passive seismic surveys (Obana et al. 2012, 2013, 2014, 2018), in which three-component, short-period (4.5 Hz) sensors were deployed in the northwestern part of the Pacific Plate. The first set consisted of linear arrays with station spacings of ~ 6 km (lines from A–A′ to E–E′ in Fig. 1) and had shorter observation periods (58 days for line A–A′, 22 days for line B–B′, 40 days for line C–C′, and 21 days for lines D–D′ and E–E′). Po waves were collected from these data sets in time series where airgun shot signals were not recorded. In the second data set, planar OBS arrays were deployed with station spacings of 25–30 km from lines from F–F′ to J–J′ (Fig. 1). The latter data set was acquired by passive seismic surveys over four periods. The OBS array locations were shifted to overlap each other, and the total observation period was 497 days (66 + 104 + 253 + 74). More than 350 OBS locations were used in the two data sets.
The horizontal orientation of each OBS in the active seismic surveys was determined using air gun shot signals (see Tonegawa et al. 2015). When the orientation could not be determined due to low signal-to-noise ratios (S/N), this study used T waves excited by earthquakes occurring in subduction zones between Mariana and Kamchatka, with magnitudes of 4.5–6.0 and focal depths shallower than 50 km to estimate the horizontal orientations of OBSs (see Tonegawa et al. 2016). The backazimuth (BAZ) range covered at most 220°. The horizontal orientations of OBSs used in passive seismic surveys were estimated using T waves. As π ambiguities exist in the orientations estimated by both techniques, the seismic phase polarities could not be identified in this study.
Po waves excited by earthquakes (magnitudes of 4.5–6.5) occurring at any depth in the subduction zones between Mariana and 180°E (east of Kamchatka) were collected from continuous OBS observation records (Additional file 1: Fig. S1). Po waves were manually selected to remove direct P arrival contamination; in the cases of earthquakes that occur above subducting slabs (hanging wall sides) or with short propagation paths between the hypocenter and OBS, Po waves are not sufficiently developed within the oceanic plate. To ensure sufficient scattering within the mantle, thereby removing contamination by direct P arrivals, earthquake signals with a straight line greater than 300 km between the hypocenter and the OBS were used.
Extraction of Pos waves
The normalized cross-spectra were used, calculated as
$$R\left( \omega \right) = \frac{{z^{*} \left( \omega \right) \cdot r\left( \omega \right)}}{{\left| {z\left( \omega \right)} \right|^{2} }},$$
(1)
$$T\left( \omega \right) = \frac{{z^{*} \left( \omega \right) \cdot t\left( \omega \right)}}{{\left| {z\left( \omega \right)} \right|^{2} }},$$
(2)
where z(ω), r(ω), and t(ω) represent the vertical, radial, and transverse components of Po coda seismograms in the frequency domain, respectively, and asterisks (*) indicate the complex conjugates. To preserve the relative amplitudes of R(ω) and T(ω), the normalization was performed using a single component, z(ω). Equations (1) and (2) are equivalent to the descriptions of radial and transverse receiver functions in the frequency domain (Langston 1979; Ammon 1991). Applying the inverse Fourier transform to Eqs. (1) and (2), the radial- and transverse-normalized cross-correlation functions (RCF and TCF, respectively) were obtained.
A Gaussian-shaped bandpass filter of 2–6 Hz was applied to calculate Eqs. (1) and (2), and time windows of − 2 to 6 s and from − 2 to 18 s were used for the vertical and horizontal components, respectively, from handpicked Po arrival times. The shorter time window of the vertical component was determined to avoid water reverberation contamination of the Po wave (Pow) and allow the first portion of Po waves to be used; Fig. 3a shows the Po waves at 0–2 s (2–6 Hz) of an earthquake aligned as a function of epicentral distance with a reduced velocity of 8 km/s alongside the Pow waves at 8–10 s. The RCF and TCF amplitudes exceed one because of the shorter time window in the vertical component; however, their relative amplitudes are preserved. Figure 3b displays the Pos waves at 2–4 s (2–6 Hz), during which the first peak corresponding to Pos waves converted at the top of the basement (Pos1). Clear Pos waves were obtained in the RCFs at 1.5–2.5 s lag time (Fig. 3c). In the Northwestern Pacific, the typical marine sediment Vp, Vp/Vs, and thickness are 1.6 km/s, 8 (Fujie et al. 2013; Tonegawa et al. 2015), and < 0.4 km (e.g., Fujiwara et al. 2007; Nakamura et al. 2013), respectively, resulting in a differential travel time of 1.75 s between vertically propagating P and S waves. This agrees well with the observed lag times of Pos1. Later phases were also observed at 2.0–3.0 s lag times, corresponding to Pos waves converted from the oceanic Moho. When a strong Pos wave was detected with a delay time of approximately 1 s after Pos1, it was defined as a Pos wave converted from the oceanic Moho (Pos2). Delay times were determined using a velocity model (Vp = 6.27 km/s, Vs = 3.49 km/s) and an oceanic crust thickness of 7 km (White et al. 1992), resulting in a differential travel time of 0.89 s between the vertically propagating P and S waves.
Furthermore, the averaged Pos1 and Pos2 amplitudes are displayed for each OBS. For each RCF trace, the maximum Pos1 and Pos2 amplitudes were measured within a time window of 0.6 s from handpicked arrival times of those waves. The averaged Pos1 and Pos2 values at each OBS are displayed to investigate the lateral variations in their amplitudes.
Estimation of anisotropy
We apply a traditional cross-correlation approach (e.g., Ando et al. 1983; Fukao 1984) for estimating the splitting parameters (the fast polarization direction and delay time) of the marine sediment layer and oceanic (igneous) crust and count the cumulative number of both parameters in three regions: two outer-rise regions and a seaward region. Both parameters were obtained at OBSs located in each region and plotted in rose diagrams and histograms, respectively. This allowed us to use splitting information at OBSs where clear Pos waves were observed, but the number of available records was minimal due to the short observation periods. Time windows of 0.6 s were used from handpicked Pos1 and Pos2 arrival times. The delay time search ranges of both layers were within 0.15 s, as determined by typical time delays at each layer and region. For each trace, the fast polarization direction and delay time of the marine sediment layer were estimated using Pos1 with a t test error estimation (e.g., Kuo et al. 1994; Chang et al. 2009; Giannopoulos et al. 2015). If C (cross-correlation coefficient) > 0.9, ∆t (delay time) ≥ 0.03 s, and ∆t error < 0.03 s, the anisotropic effect of the sediment layer was removed from Pos2 (Oda 2011) under the assumption the Pos1 and Pos2 emerging in each trace have similar incidence angles of S waves within the marine sediment and suffer similar splitting effects. The anisotropic structure of the oceanic crust was estimated using the corrected Pos2. When C > 0.9 and ∆t < 0.03 s, the anisotropic structure of the oceanic crust was also estimated using the uncorrected Pos2. Because signal-to-noise ratios of Pos2 were small compared with those of Pos1, the acceptance criterion was lowered to C > 0.8. Additional criteria were set for the Pos amplitude: (1) Pos arrival times can be handpicked, and (2) the S/N of Pos waves is greater than 2, in which S/N is defined as the ratio of the root-mean-square (RMS) amplitudes of Pos waves of 0.6 s over the noise records of − 2 to 0 s in the NCF lag time.
Additional file 1: Figure S2 demonstrates two-layer anisotropic structure estimations from a RCF-TCF pair observed at one OBS. Crosses and dash lines in Additional file 1: Fig. S2b correspond with splitting parameter measurements with uncertainties from the t test. The determined delay times and slow (negative delay time) polarization directions were − 0.03 s and − 63° from the radial direction at the sediment layer (Additional file 1: Fig. S2b) and − 0.1 s and 2° at the crustal layer (Additional file 1: Fig. S2d). Splitting parameters could be estimated within errors of ± 0.02 s and ± 20°, and linear particle motions could be obtained in the corrected Pos waveforms (Additional file 1: Fig. S2c and e).